Explanation Write the expression for velocity of the orbiter and lander. v 1 = m o v o − m l v l m s (I) Here, v 1 is the speed of the spacecraft before separation, m o is the mass of the orbiter, v o is the speed of the orbiter, m l is the mass of the lander, v l is the speed of the lander, and m s is the mass of the space station. Write the expression for velocity of the orbiter alone. v 2 = − m o v o m s (II) Here, v 2 is the speed of the spacecraft after separation. Write the expression for velocity of the composite spacecraft before separation. v s = v s x 2 + v s y 2 (III) Here, v s is the velocity of the composite spacecraft before separation. Conclusion: Substitute 784 kg + 392 kg for m s , ( − 75.4 i ^ − 214 j ^ ) m/s for v l , 784 kg for m o , ( 225 i ^ + 107 j ^ ) m/s for v o , and 392 kg for m l in the equation (I) to find v 1 . v 1 = ( 784 kg ) [ ( 225 i ^ + 107 j ^ ) m/s ] − ( 392 kg ) [ ( − 75.4 i ^ − 214 j ^ ) m/s ] 784 kg + 392 kg = ( 176400 i ^ + 83888 j ^ ) kg ⋅ m/s − ( − 29556.8 i ^ − 83888 j ^ ) kg ⋅ m/s 1176 kg = ( 175

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Chapter 9, Problem 36E

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